The value of \(\int_{-1}^{1}\displaystyle e^{|x|}\,dx\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(2(e-1)\)
Since \(e^{|-x|}=e^{|x|}\), the integrand is an even function, so
\( \displaystyle \int_{-1}^{1}e^{|x|}\,dx = 2\int_0^1 e^{|x|}\,dx \)
On [0, 1], |x| = x:
\( \displaystyle = 2\int_0^1 e^{x}\,dx \)
\( = 2\Big[e^x\Big]_0^1 = 2(e-1) \)